The idea behind RPGs is pretty cool. We get together with friends and collaboratively create a story. Our favourite fiction is a great source of inspiration in this: we can create our own epics inspired by, in the style of, or even explicitly in the setting of our favourite authors, directors and artists. But by and large, fiction tends to have a single protagonist, and that doesn’t translate well from the page or the screen to the gaming table. Even when there is also a cadre of major supporting characters, it’s generally clear who the main character is. In fiction this is a good thing, as it provides a coherent feel to the story. The major story arc relates directly to a character’s goals. We get to see into this character’s head, and it becomes possible to enjoy an entire chapter/scene/whatever that is only happening to or only relevant to that one character.Continue reading →

…Is the most amusing Google translation I saw of “Steiner, Flächen dritten Graden”. This is of course the short form of “Steiner, J. – Über die Flächen dritten Grades”, the article I have been translating from fucking German for a presentation I’m doing this week.

Anyway, most of the work is done, and my German is now a little more fluent. That is, up from “barely at all”. Most of the language is translated, leaving mostly just notation, plus a couple of technical terms like Asymptotenpuncte (asymptotic point) and Ebenenbüscheln (sheaves). You can see the original and the results here:

There were three incidents in Pakistan recently that I thought at first were the same story, they were so similar.

Thursday, August 6th. A shopkeeper in Pakistan’s southern Sindh province claims that a 60-year-old muslim woman “disrespectfully flung about pages of the Koran at his shop”, according to the BBC. The woman claims “it wasn’t the Koran she flung to the ground but a register in which the shopkeeper had listed her credit”. A crowd of people gathered at the woman’s house and threw rocks at it until police broke it up.

Two days earlier, Tuesday, August 4th. The owner of a leather factory in Punjab province takes an old calendar down from the wall. Unfortunately for him, a lot of calendars contain verses from the Koran. A factory supervisor got incensed and stirred up the workers and local residents. The owner and one other person were killed in the ensuing violence.

Three days before that, Saturday, August 1. A week after three christian youths in Gojra, eastern Pakistan are accused of burning a copy of the Koran, clerics call for their deaths. Fanatics stream in from surrounding districts. 40 houses belonging to christians are burned down, killing at least eight people, and possibly dozens.

So what’s happening here? According to local officials, none of the allegations were credible. But the BBC reports that there is “recurring evidence” that people are using Pakistan’s blasphemy laws and, in the case of the 40 christian houses, the government’s indifference to the rights of non-muslims, to settle personal scores by falsely accusing people of blasphemy. A shopkeeper and a customer have a dispute over accounts, and so the shopkeeper intimidates the customer by having people throw rocks at her house. Factory workers have a beef about their wages, so they incite violence and kill their boss. People don’t like having 50,000 christians in their town so they send thousands of them running for their lives.

This is what happens when governments pander to religious nuts. This is what happens when a government takes a stance that says “this portion of our population is better than the rest.” The saner religious folks are fine, but by and large they condone the extremists and people die. Whether it’s Najeeb Zafar in the Pakistani leather factory, or George Tiller in a Kansas church, or any number of genocides and “ethnic cleansings” around the world, or Aqsa Parvez right here in Toronto, religion kills.

In an effort to blog a bit more, and to spur myself to work harder, I’m going to try to blog more about the work I’m doing this summer.

Briefly, I’m exploring properties of subsets of the modular group, defined as the set of 2×2 matrices with determinant 1. I work with an eye toward the problem of generating congruence subgroups, which is not adequately solved. It is possible to check whether a given group is a subgroup, but it has shown to be difficult to work in the opposite direction.

This week I’m delving into Topology. Any modular subgroup can be described as a polygon on the hyperbolic plane, which in turn can be turned into a Riemann surface by identifying corresponding edges (see for example Wohlfahrt). Of particular interest is the nature of the covering of that surface. Read beneath the fold for diffeomorphisms.

Ignoring for the time being the question of whether Mathematics is a science or a meta-science or the science of science or whatever, I’ll simply don the title of “scientist” and therefore claim eligibility in Science Scouts.

I’ve started doing an intro to number theory, and one of the cool things about it is that it examines some simple questions with complicated answers. Here’s a quick example:

Show that $$n^2 – n$$ is even, for any given integer n.

And here’s the proof: we can easily see that $$n^2 – n = n(n-1)$$. Since either $$n$$ or $$n-1$$ must be even, and the product of an even number with any other number is even, their product must also be even.

This sort of problem has a property similar to many geometry problems, which is that the original statement is easily comprehensible to people without a mathematical background. In this case, the solution also is widely accessible. There are some more complex proofs, though, and I’ve put one below the fold if you’re interested.Continue reading →

In the latest issue of The Underground, UTSC’s campus paper, Erica Rodrigues writes “When freedom of speech goes too far”, a spittle-flecked protest of Peezy Myers‘ now-infamous host wafer desecration, or “Crackergate“. The article isn’t on the Underground website, so I’ve scanned it, and you can find it linked here.